# How do you sketch the angle whose terminal side in standard position passes through (-2,-3sqrt5) and how do you find sin and cos?

May 26, 2018

$\sin t = - 3 \frac{\sqrt{5}}{7}$
$\cos t = - \frac{2}{7}$

#### Explanation:

Call t the angle whose terminal side passes through
point $\left(- 2 , - 3 \sqrt{5}\right)$ --> t's terminal side lies in Quadrant 3.
$\tan t = \frac{y}{x} = \frac{- 3 \sqrt{5}}{- 2} = \frac{3 \sqrt{5}}{2}$
${\cos}^{2} t = \frac{1}{1 + {\tan}^{2} t} = \frac{1}{1 + \frac{45}{4}} = \frac{4}{49}$
$\cos t = - \frac{2}{7}$ (because t lies in Quadrant 3 --> cos t is negative)
${\sin}^{2} t = 1 - {\cos}^{2} t = 1 - \frac{4}{49} = \frac{45}{49}$
$\sin t = - \frac{3 \sqrt{5}}{7}$ (because t lies in Q.3 --> sin t is negative)